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An online e-commerce firm receives daily integer product ratings from 1 through 5 given by buyers. The daily average is the average of the ratings given on that day. The cumulative average is the average of all ratings given on or before that day. The rating system began on Day 1, and the cumulative averages were 3 and 3.1 at the end of Day 1 and Day 2, respectively. The distribution of ratings on Day 2 is given in the figure below.

Practice Question - 9 (Chart) | 100 DILR Questions for CAT Preparation The following information is known about ratings on Day 3.
1. 100 buyers gave product ratings on Day 3.
2. The modes of the product ratings were 4 and 5.
3. The numbers of buyers giving each product rating are non-zero multiples of 10.
4. The same number of buyers gave product ratings of 1 and 2, and that number is half the number of buyers who gave a rating of 3.

Q1: How many buyers gave ratings on Day 1?

View Answer

Ans: 150
From the given chart, we can find the average rating on day 2:
Practice Question - 9 (Chart) | 100 DILR Questions for CAT Preparation
We are given the cumulative average of day 1 and day 2 as 3.1, and the average at the end of day 1 is 3.
Let's take the number of ratings received on day 1 as x; using this overall average and the average on day 2, we get the equation:
Practice Question - 9 (Chart) | 100 DILR Questions for CAT Preparation
3x + 170 = 3.1x + 155
15 = 0.1 x
x = 150
Therefore, the number of ratings received on day 1 is 150.

Q2: What is the daily average rating of Day 3?
(a) 3.6
(b) 3.0
(c) 3.2
(d) 3.5

View Answer

Ans: (a)
We are given that on day 3, a total of 100 ratings came in
The modes were 4 and 5, meaning that an equal number of 4 and 5 ratings came in; let it be 10b (since we are given that all ratings were non-zero multiples of 10)
Let's take the number of 1 and 2 ratings as 10a each, giving the number of 3 ratings as 20a
Adding all of these up: 10a + 10a + 20a + 10b + 10b = 100
40a + 20b = 100
2a+b = 5
The only integer combination for a and b, without them being zero, is a being 1 and b being 3 or a=2 and b=1
But taking b as 1 would make 3 as the mode rating, so we can not consider the latter case.
We are giving 10 - 1 ratings, 10 - 2 ratings, 20 - 3 ratings, 30 - 4 ratings, and 30 - 5 ratings.
The average would be Practice Question - 9 (Chart) | 100 DILR Questions for CAT Preparation
Therefore, Option (a) is the correct answer.

Q3: What is the median of all ratings given on Day 3?

View Answer

Ans: 4
As deduced in the previous question, there were 10 1 ratings, 10 2 ratings, 20 3 ratings, 30 4 ratings, and 30 5 ratings.
The median would be the 50th and 51st ratings' average when arranged in ascending/descending order.
Both of which would be 4
Practice Question - 9 (Chart) | 100 DILR Questions for CAT Preparation Therefore, 4 is the correct answer

Q4: Which of the following is true about the cumulative average ratings of Day 2 and Day 3?
(a) The cumulative average of Day 3 increased by less than 5% from Day 2.
(b) The cumulative average of Day 3 decreased from Day 2.
(c) The cumulative average of Day 3 increased by a percentage between 5% and 8% from Day 2.
(d) The cumulative average of Day 3 increased by more than 8% from Day 2.

View Answer

Ans: (c)
The cumulative average rating at the end of day 3 would be Practice Question - 9 (Chart) | 100 DILR Questions for CAT Preparation

[The cumulative average rating on day 2= 3.1
Number of ratings received by day 2= 200]
Practice Question - 9 (Chart) | 100 DILR Questions for CAT Preparation
The increase in the cumulative average from day 2 to day 3 can be calculated as
Which aligns with the statement given in option C.
Therefore, Option C is the correct answer.

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FAQs on Practice Question - 9 (Chart) - 100 DILR Questions for CAT Preparation

1. What is Chart Based Question in CAT?

Ans.Chart Based Questions in the CAT exam are designed to assess a candidate's ability to interpret data presented in various forms such as graphs, charts, and tables. These questions require analytical skills to extract relevant information and draw conclusions based on the presented data.

2. How can I effectively prepare for Chart Based Questions in the CAT exam?

Ans.Effective preparation for Chart Based Questions involves practicing with a variety of data interpretations, such as line graphs, bar charts, and pie charts. Candidates should familiarize themselves with common data trends and practice solving questions within a timed environment to enhance speed and accuracy.

3. What types of charts are commonly used in CAT Chart Based Questions?

Ans.Common types of charts used in CAT Chart Based Questions include bar charts, line graphs, pie charts, and tables. Understanding how to read and interpret these charts is crucial for answering the questions correctly.

4. Are there any specific strategies to solve Chart Based Questions quickly?

Ans.Yes, some strategies include quickly identifying the key data points, summarizing the information in your own words, and looking for trends rather than getting bogged down in details. Practice with timed quizzes can also help in developing these strategies.

5. How important are Chart Based Questions in the overall CAT exam scoring?

Ans.Chart Based Questions are significant in the CAT exam as they test quantitative and analytical skills, which are crucial for management studies. While each question carries a specific weight, performing well in this section can help boost overall scores, especially for candidates aiming for high percentiles.

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